A self-contained proof to Martio's conjecture in the class of BLD-maps

TL;DR

This paper presents a new, self-contained proof of Martio's conjecture for BLD-maps, avoiding the traditional reliance on continuity modulus estimates from 1970.

Contribution

It offers a novel proof approach for Martio's conjecture within the class of BLD-maps, independent of previous continuity modulus methods.

Findings

Proof of Martio's conjecture for BLD-maps established

New proof technique independent of 1970 modulus estimates

Enhanced understanding of BLD-map properties

Abstract

We provide a self-contained proof to so-called Martio's conjecture in the class of mappings of bounded length distortion. Unlike the earlier proofs, our proof is not based on the modulus of continuity estimate of Martio from 1970.